Ho il piacere di invitarvi al seguente seminario, che si terrà lunedì 21 ottobre, alle ore 15:00, nell'aula 2BC30 della Torre Archimede presso il Dipartimento di Matematica dell'Universita` degli Studi di Padova. SPEAKER: Dott.ssa Alessandra Cipriani AFFILIATION: Institute of Mathematics, University of Zurich TITLE: Thick points for a Gaussian Free Field in 4 dimensions ABSTRACT: This joint work with Rajat Subhra Hazra is concerned with the study of the fractal dimension of thick points for a 4-dimensional Gaussian Free Field. We adopt the definition of Gaussian Free Field on R^4 introduced by Chen and Jakobson (2012) viewed as an abstract Wiener space with underlying Hilbert space H^2(R^4). We can prove that for 0 ≤ a ≤ 4 the Hausdorff dimension of the set of a-high points is 4 − a, and we show that this set is the support of the 4-dimensional Liouville quantum gravity measure. -- Alessandra Bianchi Dip. di Matematica Pura e Applicata Università di Padova Via Trieste, 63 - 35121 Padova, Italy phone: +39 049 827 14 06 fax: +39 049 827 14 28 e-mail: bianchi@math.unipd.it http://www.math.unipd.it/~bianchi/